The former Utah Jazz guard and three-time All-Star was part of arguably the biggest trade of the offseason, with the Jazz receiving three unprotected first-round picks.
Mitchell had been one of the most desirable names on the market after it became clear the Jazz were entering a rebuild following their trade of three-time Defensive Player of the Year Rudy Gobert to the Minnesota Timberwolves.
Despite being "excited" to be in Cleveland, Mitchell – who is from New York – told ESPN he was close to signing for the Knicks.
"Very close, I won't say more than that, I know a little bit more than most, but definitely very close," he said. "I was truly excited when I got traded [to the Cavaliers], but we were, it was, it was close [to the Knicks]."
He also disputed comments from Jazz CEO Danny Ainge, who claimed earlier in the week that Utah's players last season "didn't really believe in each other".
"I don't think we didn't believe [in each other]," Mitchell riposted. "I said at the end of the season, 'don't trade [Gobert]. Let's figure this out, let's do.' And that didn't happen.
"For [Ainge] to say that after six months around the team, I disagree. But you know, at the end of the day, that's his decision."
The 25-year-old spent five seasons in Utah, averaging 23.9 points per game, as well as 4.2 rebounds and 4.5 assists.